2/3m=2-5/m

Solution for 2/3m=2-5/m equation:

2/3m=2-5/m

We move all terms to the left:

2/3m-(2-5/m)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

2/3m-(-5/m+2)=0

We get rid of parentheses

2/3m+5/m-2=0

We calculate fractions


2m/3m^2+15m/3m^2-2=0

We multiply all the terms by the denominator


2m+15m-2*3m^2=0

We add all the numbers together, and all the variables

17m-2*3m^2=0

Wy multiply elements

-6m^2+17m=0

a = -6; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-6)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-6}=\frac{-34}{-12}
=2+5/6
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-6}=\frac{0}{-12}
=0
$